Let's solve the problem step-by-step.
1. Simplify [tex]\(\frac{4}{16}\)[/tex] to its lowest terms:
To simplify a fraction, we need to divide both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD).
Here, the numerator is 4 and the denominator is 16. The GCD of 4 and 16 is 4.
[tex]\[
\frac{4 \div 4}{16 \div 4} = \frac{1}{4}
\][/tex]
Therefore, [tex]\(\frac{4}{16}\)[/tex] simplified to its lowest terms is [tex]\(\frac{1}{4}\)[/tex].
2. Find an equivalent fraction that has a denominator of 32:
To find an equivalent fraction with a specific denominator, you can set up the following proportion:
[tex]\[
\frac{1}{4} = \frac{x}{32}
\][/tex]
To find [tex]\(x\)[/tex], we solve the proportion by cross-multiplying:
[tex]\[
1 \cdot 32 = 4 \cdot x
\][/tex]
[tex]\[
x = \frac{32}{4} = 8
\][/tex]
So, an equivalent fraction for [tex]\(\frac{1}{4}\)[/tex] with a denominator of 32 is [tex]\(\frac{8}{32}\)[/tex].
Therefore, the solution is:
- The simplified form of [tex]\(\frac{4}{16}\)[/tex] is [tex]\(\frac{1}{4}\)[/tex].
- An equivalent fraction with a denominator of 32 is [tex]\(\frac{8}{32}\)[/tex].
Thus, the correct choice is:
[tex]\[ \boxed{\frac{1}{4}, \frac{8}{32}} \][/tex]
